Re: New band problems...
I wouldn't walk out until you have another gig lined up. But that should be a last resort. As far as the "my" band thing goes...yea you're too sensitive there. Give that up. That is said all the time and it's a term if endearment, not ownership. Sometimes it's in your best interest to give the guy enough rope to hang himself with. Perhaps, instead of thinking about leaving, how about coming up with a better singer to rehearse? That's being proactive. Get the existing singer something to think about by bringing in some competition. That way you're not a problem maker, you're a solution maker, and may the best man win. You have to tread lightly here, there is a very strong possibility of you alienating the wrong people by being too controlling.
Point out issues, and offer possible solutions, without pointing fingers or naming names. How you word things is crucial. I would avoid the whole "problem" scenario and simply say hey guys you should hear this guy sing, sidestepping the whole problem issue. Your actions by lining another up will tell everyone where your head is without you having to detail blow by blow reasons why you aren't happy.